Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense

• Autorzy: Suzuki T.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove that a mapping T on a metric space is contractive with respect to a τ-distance if and only if it is Kannan with respect to a τ-distance.

Słowa kluczowe

EN

contractive mapping; Kannan mapping; fixed point

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2005
• Tom: Vol. 45, [Z] 1
• Strony: 45--58
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Suzuki T.

• Department of Mathematics, Kyushu Institute of Technology,

Bibliografia

• [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181.
• [2] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251.
• [3] E. H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), 974-979.
• [4] D. Downing and W. A. Kirk, A generalization of Caristi’s theorem with applications to non-linear mapping theory, Pacific J. Math. 69 (1977), 339-346.
• [5] M. Edelstein, An extension of Banach’s contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7-10.
• [6] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353.
• [7] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443-474.
• [8] O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44 (1996), 381-391.
• [9] R. Kannan, Some results on fixed points - II, Amer. Math. Monthly 76 (1969), 405-408.
• [10] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
• [11] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
• [12] N. Shioji, T. Suzuki and W. Takahashi, Contractive mappings, Kannan mappings and metric completeness, Proc. Amer. Math. Soc. 126 (1998), 3117-3124.
• [13] P. V. Subrahmanyam, Completeness and fixed-points, Monatsh. Math. 80 (1975), 325-330.
• [14] T. Suzuki, Fixed point theorems in complete metric spaces, in Nonlinear Analysis and Convex Analysis (W. Takahashi Ed.), RIMS Kokyuroku 939 (1996), 173-182.
• [15] T. Suzuki, Several fixed point theorems in complete metric spaces, Yokohama Math. J. 44 (1997), 61-72.
• [16] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl. 253 (2001), 440-458.
• [17] T. Suzuki, On Downing-Kirk’s theorem, J. Math. Anal. Appl. 286 (2003), 453-458.
• [18] T. Suzuki, Several fixed point theorems concerning τ -distance, Fixed Point Theory Appl. 2004 (2004), 195-209.
• [19] T. Suzuki and W. Takahashi, Fixed point theorems and characterizations of metric completeness, Topol. Methods Nonlinear Anal. 8 (1996), 371-382.
• [20] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.
• [21] D. Tataru, Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms, J. Math. Anal. Appl. 163 (1992), 345-392.
• [22] C. K. Zhong, On Ekeland’s variational principle and a minimax theorem, J. Math. Anal. Appl. 205 (1997), 239-250.